Alright, first thoughts: this is a VERY cool concept. Took me a bit to orient myself, but when I 'got' it, I was amazed.
That said, it feels like it might be a bit too easy to softlock yourself: just place some blocks around yourself or the key so that you leave some 1-blocks gaps that you can never fill. That's basically how I lost in my two attempts. I'm not sure if there's some tetris-like mechanic for clearing blocks, does the game ever explain it? (I haven't read the tutorial very thoroughly, sorry).
Anyway, when you softlock like this, I think the only way to lose is to intentionally stack up pieces, which feels bad. Also, now I wonder if using tetraminos instead of weird 6-block pieces would've helped...
Another thing: I wish I could keep pressing the down arrow to make the piece fall faster.
Anyway, all of that doesn't matter, juggling two different screens at once is so novel (to me, anyway) that I can't help but like your game.